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Classification of 4 -dimensional homogeneous weakly Einstein manifolds

Teresa Arias-Marco, Oldřich Kowalski (2015)

Czechoslovak Mathematical Journal

Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension 4 is the most interesting case, where...

Classification of 4-dimensional homogeneous D'Atri spaces

Teresa Arias-Marco, Oldřich Kowalski (2008)

Czechoslovak Mathematical Journal

The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold ( M , g ) satisfying the first odd Ledger condition is said to be of type 𝒜 . The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in the papers...

Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection ∇ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the ∇ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of ∇ -parallel vector fields.

Commuting linear operators and algebraic decompositions

Rod A. Gover, Josef Šilhan (2007)

Archivum Mathematicum

For commuting linear operators P 0 , P 1 , ⋯ , P ℓ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition P = P 0 P 1 ⋯ P ℓ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem P u = f reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures ( g , ± ω ) with constant scalar curvature is either Einstein, or the dual field of ω is Killing. Next, let ( M n , g ) be a complete and connected Riemannian manifold of dimension at least 3 admitting a pair of Einstein-Weyl structures ( g , ± ω ) . Then the Einstein-Weyl vector field E (dual to the 1 -form ω ) generates an infinitesimal harmonic transformation if and only if E is Killing.

Conformal and related changes of metric on the product of two almost contact metric manifolds.

David E. Blair, José Antonio Oubiña (1990)

Publicacions Matemàtiques

This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, α-Sasakian and β-Kenmotsu structures.

Currently displaying 61 – 80 of 478